= PDAF_diag_effsample = 

This page documents the routine `PDAF_diag_effsample` of PDAF, which was introduced with PDAF V1.12.

This routine computes the effective sample size of a particle filter as defined in Doucet et al. 2001 p. 333. 

The effective sample size is a diagnostic quantity used in particle filter. It is defined as the inverse of the sum of the squared particle filter weights:
{{{
n_eff = 1 / (Sum_i=1,N w_i^2)
}}}
where `w_i` is the weight of particle with index i and `N` is the number of particles. If all weights are identical, it is `n_eff=N` and a particle file analysis step will have no influence. If `n_eff=1`, a single particle contains all weight, such that the sample of particle collapeses.

The routine is typically called during the analysis step of a particle filter, e.g. in the analysis step of NETF and LNETF.

The interface is the following:
{{{
  SUBROUTINE PDAF_diag_effsample(dim_sample, weights, n_eff)
}}}
with the following arguments:
 * `dim_sample` : `integer, intent(in)`[[BR]] Number of particles
 * `weights` : `real, intent(in), dimension(dim_sample)`[[BR]] Weights of the particles
 * `n_eff` : `real, intent(out)`[[BR]] Effective sample size